The idea of a “soul” (neshamah in Hebrew) is fundamental to Judaism, which sees the soul as eternal. Although clear references to the human soul do appear in the Bible, most of what the Jewish tradition teaches about the soul comes from rabbinical (post-Biblical) times. The soul comes from God, and it precedes the existence of a human body. As for where the soul is headed after this life, we are told in Ecclesiastes that the soul returns to God (thus, the idea of an afterlife): “The dust returns to the earth as it was, and the spirit returns to God who gave it” (12:7).
The Soul's Components
The Jewish conception of a soul is rather unique. In Judaism, the soul is not indivisible. Rather, it is more like an amalgamation of five basic elements that are in turn subdivided into even more elements. This is a very complicated subject that has a lot to do with Kabbalah (Jewish mysticism) and that will only be briefly summarized here.
The lowest constituent of the soul is nefesh, and it is the soul's most physical aspect. In ascending order, the soul's other, more spiritual elements are ruach, neshamah, chayah, and yechidah. To refer to all five of these components, you can use the term narachai (an acronym of the five terms). Since the naranchai is numinous, it seeks spirituality, which is why humans seek to pursue the spiritual.
After a person dies, that person's naranchai will desire to leave the physical body. If the person has led a spiritual life, this desire will be fulfilled. However, the naranchai of those who were focused on the material aspect of the world may remain rooted to the physical. (It gets even more complex than this, but the point is that there is a soul within each of us. To what extent it reaches its spiritual destination depends upon how we lived our lives.)